### Abstract

Fullerene molecules such as C _{60} are large nearly spherical shells of carbon atoms. Pairs of such molecules have a strong long-range van der Waals attraction that can produce scattering or binding into molecular crystals. A simplified classical-electrodynamics model for a fullerene is a spherical metal shell, with uniform electron density confined between outer and inner radii (just as a simplified model for a nearly spherical metallic nanocluster is a solid metal sphere or filled shell). For the spherical-shell model, the exact dynamic multipole polarizabilities are all known analytically. From them, we can derive exact analytic expressions for the van der Waals coefficients of all orders between two spherical metal shells. The shells can be identical or different, and hollow or filled. To connect the model to a real fullerene, we input the static dipole polarizability, valence electron number and estimated shell thickness t of the real molecule. Our prediction for the leading van der Waals coefficient C _{6} between two C _{60} molecules ((1.30±0.22)×10 ^{5}hartreebohr ^{6}) agrees well with a prediction for the real molecule from time-dependent density functional theory. Our prediction is remarkably insensitive to t. Future work might include the prediction of higher-order (e.g. C _{8} and C _{10}) coefficients for C _{60}, applications to other fullerenes or nearly spherical metal clusters, etc. We also make general observations about the van der Waals coefficients.

Original language | English |
---|---|

Article number | 424207 |

Journal | Journal of Physics Condensed Matter |

Volume | 24 |

Issue number | 42 |

DOIs | |

Publication status | Published - Oct 24 2012 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Materials Science(all)
- Medicine(all)

### Cite this

*Journal of Physics Condensed Matter*,

*24*(42), [424207]. https://doi.org/10.1088/0953-8984/24/42/424207

**Spherical-shell model for the vanderWaals coefficients between fullerenes and/or nearly spherical nanoclusters.** / Perdew, John P.; Tao, Jianmin; Hao, Pan; Ruzsinszky, Adrienn; Csonka, G.; Pitarke, J. M.

Research output: Contribution to journal › Article

*Journal of Physics Condensed Matter*, vol. 24, no. 42, 424207. https://doi.org/10.1088/0953-8984/24/42/424207

}

TY - JOUR

T1 - Spherical-shell model for the vanderWaals coefficients between fullerenes and/or nearly spherical nanoclusters

AU - Perdew, John P.

AU - Tao, Jianmin

AU - Hao, Pan

AU - Ruzsinszky, Adrienn

AU - Csonka, G.

AU - Pitarke, J. M.

PY - 2012/10/24

Y1 - 2012/10/24

N2 - Fullerene molecules such as C 60 are large nearly spherical shells of carbon atoms. Pairs of such molecules have a strong long-range van der Waals attraction that can produce scattering or binding into molecular crystals. A simplified classical-electrodynamics model for a fullerene is a spherical metal shell, with uniform electron density confined between outer and inner radii (just as a simplified model for a nearly spherical metallic nanocluster is a solid metal sphere or filled shell). For the spherical-shell model, the exact dynamic multipole polarizabilities are all known analytically. From them, we can derive exact analytic expressions for the van der Waals coefficients of all orders between two spherical metal shells. The shells can be identical or different, and hollow or filled. To connect the model to a real fullerene, we input the static dipole polarizability, valence electron number and estimated shell thickness t of the real molecule. Our prediction for the leading van der Waals coefficient C 6 between two C 60 molecules ((1.30±0.22)×10 5hartreebohr 6) agrees well with a prediction for the real molecule from time-dependent density functional theory. Our prediction is remarkably insensitive to t. Future work might include the prediction of higher-order (e.g. C 8 and C 10) coefficients for C 60, applications to other fullerenes or nearly spherical metal clusters, etc. We also make general observations about the van der Waals coefficients.

AB - Fullerene molecules such as C 60 are large nearly spherical shells of carbon atoms. Pairs of such molecules have a strong long-range van der Waals attraction that can produce scattering or binding into molecular crystals. A simplified classical-electrodynamics model for a fullerene is a spherical metal shell, with uniform electron density confined between outer and inner radii (just as a simplified model for a nearly spherical metallic nanocluster is a solid metal sphere or filled shell). For the spherical-shell model, the exact dynamic multipole polarizabilities are all known analytically. From them, we can derive exact analytic expressions for the van der Waals coefficients of all orders between two spherical metal shells. The shells can be identical or different, and hollow or filled. To connect the model to a real fullerene, we input the static dipole polarizability, valence electron number and estimated shell thickness t of the real molecule. Our prediction for the leading van der Waals coefficient C 6 between two C 60 molecules ((1.30±0.22)×10 5hartreebohr 6) agrees well with a prediction for the real molecule from time-dependent density functional theory. Our prediction is remarkably insensitive to t. Future work might include the prediction of higher-order (e.g. C 8 and C 10) coefficients for C 60, applications to other fullerenes or nearly spherical metal clusters, etc. We also make general observations about the van der Waals coefficients.

UR - http://www.scopus.com/inward/record.url?scp=84867240351&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867240351&partnerID=8YFLogxK

U2 - 10.1088/0953-8984/24/42/424207

DO - 10.1088/0953-8984/24/42/424207

M3 - Article

C2 - 23032569

AN - SCOPUS:84867240351

VL - 24

JO - Journal of Physics Condensed Matter

JF - Journal of Physics Condensed Matter

SN - 0953-8984

IS - 42

M1 - 424207

ER -